<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\usepackage{epsfig}
\newcommand{\un}{\underline}
\begin{document}
\parindent=0pt


\begin{center}
\textbf{Vector Fields}

\textit{\textbf{Scalar and Vector Fields}}
\end{center}

\textbf{Question}

Describe the streamlines of the following velocity field.

$\un{v}(x,y,z) = y \un{i} -y\un{j} -y\un{k}$


\textbf{Answer}

The streamlines satisfy $dx=-dy=-dz$. Thus $y+x=C_1$, $z+x=C_2$.

The streamlines are straight lines parallel to $\un{i} -\un{j} -\un{k}$.

\end{document}

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